A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $300 with a standard deviation of $48. A random sample of 144 checking accounts is selected.
a. What is the probability that the sample mean will be more than $306.60?
b. What is the probability that the sample mean will be less than $308?
c. What is the probability that the sample mean will be between $302 and $308?
d. What is the probability that the sample mean will be at least $296?